On the Classical Schrödinger Equation
Abstract
In this paper, the classical Schrödinger equation (CSE), which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an additional singlevalued condition for the Hamilton’s principal function, the CSE is obtained. This additional assumption implies inherent nonclassical features on the description of the dynamics obtained from the CSE: the trajectories do not cross in the configuration space. Second, departing from Bohmian mechanics and invoking the quantumtoclassical transition, the CSE is obtained in a natural way for the center of mass of a quantum system with a large number of identical particles. This quantum development imposes the condition of dealing with a narrow wave packet, which implicitly avoids the nonclassical features mentioned above. We illustrate all the above points with numerical simulations of the classical and quantum Schrödinger equations for different systems.
 Publication:

Fluctuation and Noise Letters
 Pub Date:
 October 2016
 DOI:
 10.1142/S0219477516400113
 arXiv:
 arXiv:1607.00168
 Bibcode:
 2016FNL....1540011B
 Keywords:

 Quantum and classical Schrödinger equations;
 quantumtoclassical transition;
 quantum classical trajectories;
 decoherence in the center of mass;
 Quantum Physics
 EPrint:
 11 pages, 7 figures